Fractional Programming

Frenk, J. B. G.; Schaible, Siegfried

doi:10.1007/0-387-23393-8_8

Cited by 28 publications

(12 citation statements)

References 45 publications

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“…The objective function of problem P 2 is now explicit, but it is still non-convex, and potentially possessing several local optima. More precisely, this problem belongs to the class of fractional programming problems [12]. As many other global optimization problems, fractional programming problems involving a sum of ratios are difficult problems, because many local minima can exist.…”

Section: (α)mentioning

confidence: 99%

Optimization of network protection against virus spread

Gourdin

Omić

Mieghem

2011

2011 8th International Workshop on the Design of Reliable Communication Networks (DRCN)

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Abstract-The effect of virus spreading in a telecommunication network, where a certain curing strategy is deployed, can be captured by epidemic models. In the N -intertwined model proposed and studied in [1], [2], the probability of each node to be infected depends on the curing and infection rate of its neighbors. In this paper, we consider the case where all infection rates are equal and different values of curing rates can be deployed within a given budget, in order to minimize the overall infection of the network. We investigate this difficult optimization together with a related problem where the curing budget must be minimized within a given level of network infection. Some properties of these problems are derived and several solution algorithms are proposed. These algorithms are compared on two real world network instances, while Erdös-Rényi graphs and some special graphs such as the cycle, the star, the wheel and the complete bipartite graph are also addressed.

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Section: (α)mentioning

confidence: 99%

Optimization of network protection against virus spread

Gourdin

Omić

Mieghem

2011

2011 8th International Workshop on the Design of Reliable Communication Networks (DRCN)

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“…The goals may include, for instance, maximization of output to input, maximization of return to risk, maximization of the rate of growth of national income, and maximization of profit to cost. For detailed examples, see Frenk and Schaible (2001), Stancu-Minasian (1997), Steuer (1986) and references therein.…”

Section: Introductionmentioning

confidence: 98%

“…From Frenk and Schaible (2001), Schaible (1995) and Stancu-Minasian (1997), problem (P) arises in practice in situations where several ratios are to be simultaneously optimized, but these ratios are not simultaneously optimized at any single point in Y. The ratios themselves may represent a wide variety of economic, financial or production measures.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, for certain cases, Kornbluth and Steuer (1981) have developed a procedure for generating the set of all weakly efficient vertices of a multiobjective linear fractional program. For full details of the available research on multiobjective linear fractional programs, see Stancu-Minasian (1997), Frenk and Schaible (2001) and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…; pg, where y 2 Y, the point y is said to dominate the point y 0 . The goal of problem (P) is to generate the set Y E of all efficient points for the problem or to generate at least a representative subset of Y E (Frenk and Schaible, 2001). When Y is a polyhedron and, for each i ¼ 1; 2; .…”

Section: Introductionmentioning

confidence: 99%

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A global optimization approach for generating efficient points for multiobjective concave fractional programs

Benson

2005

J. Multi-Crit. Decis. Anal.

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In this article, we present a global optimization approach for generating efficient points for multiobjective concave fractional programming problems. The main work of the approach involves solving an instance of a concave multiplicative fractional program (W). Problem (W) is a global optimization problem for which no known algorithms are available. Therefore, to render the approach practical, we develop and validate a branch and bound algorithm for globally solving problem (W). To illustrate the performance of the global optimization approach, we use it to generate efficient points for a sample multiobjective concave fractional program.

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A Polynomial Algorithm for a Class of 0–1 Fractional Programming Problems Involving Composite Functions, with an Application to Additive Clustering

Hansen

Meyer

2014

Clusters, Orders, and Trees: Methods and Applications

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We derive conditions on the functions ', , v and w such that the 0-1 fractional programming problem max w.x/ on OE0I C1/. In particular we show that when ' is convex and increasing, is concave, increasing and strictly positive, v and w are supermodular and either v or w has a monotonicity property, then the 0-1 fractional programming problem can be solved in polynomial time in essentially the same time complexity than to solve the fractional programming problem max, and this even if ' and are nonrational functions provided that it is possible to compare efficiently the value of the objective function at two given points of f0I 1g n . We apply this result to show that a 0-1 fractional programming problem arising in additive clustering can be solved in polynomial time.

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Fractional Programming

Cited by 28 publications

References 45 publications

Optimization of network protection against virus spread

Optimization of network protection against virus spread

A global optimization approach for generating efficient points for multiobjective concave fractional programs

A Polynomial Algorithm for a Class of 0–1 Fractional Programming Problems Involving Composite Functions, with an Application to Additive Clustering

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